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In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…

Machine Learning · Statistics 2025-07-01 Yingyuan Li , Aokun Wang , Zhongjian Wang

We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection…

Statistical Mechanics · Physics 2010-04-05 J. Bouttier , P. Di Francesco , E. Guitter

The paper considers the problem of planning a set of non-conflict trajectories for the coalition of intelligent agents (mobile robots). Two divergent approaches, e.g. centralized and decentralized, are surveyed and analyzed. Decentralized…

Artificial Intelligence · Computer Science 2017-07-21 Anton Andreychuk , Konstantin Yakovlev

The next generation of large-scale spectroscopic survey experiments such as DESI, will use thousands of fiber positioner robots packed on a focal plate. In order to maximize the observing time with this robotic system we need to move in…

Instrumentation and Methods for Astrophysics · Physics 2015-06-23 Laleh Makarem , Jean-Paul Kneib , Denis Gillet , Hannes Bleuler , Mohamed Bouri , Philipp Hörler , Laurent Jenni , Francisco Prada , Justo Sanchez

We present a planning framework designed for humanoid navigation over challenging terrain. This framework is designed to plan a traversable, smooth, and collision-free path using a 2.5D height map. The planner is comprised of two stages.…

Robotics · Computer Science 2022-03-02 Stephen McCrory , Bhavyansh Mishra , Jaehoon An , Robert Griffin , Jerry Pratt , Hakki Erhan Sevil

This paper addresses the problem of planning a safe (i.e., collision-free) trajectory from an initial state to a goal region when the obstacle space is a-priori unknown and is incrementally revealed online, e.g., through line-of-sight…

Robotics · Computer Science 2018-04-17 Lucas Janson , Tommy Hu , Marco Pavone

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths…

Computational Geometry · Computer Science 2015-04-22 Kiril Solovey , Jingjin Yu , Or Zamir , Dan Halperin

Proper path planning is the first step of robust and efficient autonomous navigation for mobile robots. Meanwhile, it is still challenging for robots to work in a complex environment without complete prior information. This paper presents…

Robotics · Computer Science 2020-09-17 Wenjian Hao , Rongyao Wang , Alexander Krolicki , Yiqiang Han

Consider being given a mapping \phi from the unit sphere S^{d-1}, d>2, to the smooth boundary of a simply-connected region \Omega in R^d. We consider the problem of constructing an extension \Phi from the unit ball B_d to \Omega. The…

Numerical Analysis · Mathematics 2011-06-20 Kendall Atkinson , Olaf Hansen

Mobile robots dedicated in security tasks should be capable of clearly perceiving their environment to competently navigate within cluttered areas, so as to accomplish their assigned mission. The paper in hand describes such an autonomous…

This paper considers the problem of optimally deploying omnidirectional sensors, with potentially limited sensing radius, in a network-like environment. This model provides a compact and effective description of complex environments as well…

Optimization and Control · Mathematics 2010-06-18 Luca Greco , Matteo Gaeta , Benedetto Piccoli

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

Data Structures and Algorithms · Computer Science 2022-09-27 Marin Bougeret , Jérémy Omer , Michael Poss

A novel mechanism to derive self-entanglement-free (SEF) path for tethered differential-driven robots is proposed in this work. The problem is tailored to the deployment of tethered differential-driven robots in situations where an…

Robotics · Computer Science 2023-08-31 Tong Yang , Jiangpin Liu , Yue Wang , Rong Xiong

We develop a gradient-like algorithm to minimize a sum of peer objective functions based on coordination through a peer interconnection network. The coordination admits two stages: the first is to constitute a gradient, possibly with…

Optimization and Control · Mathematics 2023-07-19 Sandushan Ranaweera , Chathuranga Weeraddana , Prathapasinghe Dharmawansa , Carlo Fischione

We present a number of breakthroughs for coordinated motion planning, in which the objective is to reconfigure a swarm of labeled convex objects by a combination of parallel, continuous, collision-free translations into a given target…

Computational Geometry · Computer Science 2018-01-08 Erik D. Demaine , Sándor P. Fekete , Phillip Keldenich , Henk Meijer , Christian Scheffer

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable…

Robotics · Computer Science 2021-06-08 Alexander Botros , Stephen L. Smith

We consider path planning for a rigid spatial robot moving amidst polyhedral obstacles. Our robot is either a rod or a ring. Being axially-symmetric, their configuration space is R^3 x S^2 with 5 degrees of freedom (DOF). Correct, complete…

Computational Geometry · Computer Science 2019-06-10 Ching-Hsiang Hsu , Yi-Jen Chiang , Chee Yap

This paper aims to improve the computational efficiency of motion planning for mobile robots with non-trivial dynamics through the use of learned controllers. Offline, a system-specific controller is first trained in an empty environment.…

In this work a discrete counterpart to the continuous harmonic potential field approach is suggested. The extension to the discrete case makes use of the strong relation HPF-based planning has to connectionist artificial intelligence (AI).…

Robotics · Computer Science 2016-08-23 Ahmad A. Masoud

We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the linear-time shortest-path algorithm of Henzinger, Klein, Subramanian, and Rao [STOC'94]. The second is Fakcharoenphol…

Data Structures and Algorithms · Computer Science 2014-04-04 Shay Mozes , Yahav Nussbaum , Oren Weimann